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Momentum and Impulse

Using p = mv and impulse FΔt = Δp for impacts and safety design.

  • Define and explain Momentum and Impulse in your own words
  • Use key terms such as impulse accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Momentum and Impulse: using p = mv and impulse FΔt = Δp for impacts and safety design.

Definition: Momentum and Impulse

Using p = mv and impulse FΔt = Δp for impacts and safety design.

Key ideas

Momentum is conserved in every collision

Total momentum before an interaction equals total momentum after, provided no external impulse acts. In elastic collisions kinetic energy is conserved too; in inelastic collisions some becomes heat and sound. Crumple zones lengthen impact time, cutting the peak force via F = Δp/Δt — the physics that saves lives.

Circular motion needs a constant centre-seeking force

An object circling at steady speed is accelerating because its velocity direction keeps changing. The centripetal acceleration is v²/r towards the centre, so the required force is F = mv²/r. Remove the force — cut the string — and the object flies off along a tangent, which is why mud flings off a spinning wheel.

Key term — impulse: Force × time (FΔt), equal to the change in momentum.

Worked example: Momentum and Impulse

Why do airbags reduce injury in a crash?

They increase the time over which momentum changes, so the average force on the passenger is smaller.

Answer: They increase the time over which momentum changes, so the average force on the passenger is smaller.

Common mistakes
  • Treating momentum as a scalar Momentum has direction; opposite momenta subtract, which is why head-on collisions need a sign convention.
  • Inventing an outward 'centrifugal force' In an inertial frame there is only the inward centripetal force — the outward feeling is just inertia resisting the turn.

Practice

A 1200 kg car rounds a bend of radius 50 m at 20 m/s. Find the centripetal force.
F = mv²/r.

(1200 × 400) ÷ 50 = 480,000 ÷ 50 = 9600 N.

A 0.2 kg mass on a spring (k = 80 N/m) oscillates. Calculate the period.
T = 2π√(m/k).

√(0.2 ÷ 80) = √0.0025 = 0.05, so T = 2π × 0.05 ≈ 0.31 s.

A 0.5 kg ball moving at 6 m/s is stopped in 0.2 s. Find the average force.
Impulse = change in momentum.

Δp = 0.5 × 6 = 3 kg m/s; F = 3 ÷ 0.2 = 15 N.

Two trolleys (2 kg at 3 m/s, 1 kg stationary) stick together after colliding. Find their combined speed.
Conserve total momentum.

Before: 2 × 3 = 6 kg m/s. After: 3 kg × v = 6, so v = 2 m/s.

Quick check

Momentum and Impulse — quick check

Which of these best defines "impulse"?

Force × time (FΔt), equal to the change in momentum.

In SHM, where are speed and acceleration greatest?

Speed is greatest at equilibrium (maximum kinetic energy); acceleration is greatest at maximum displacement (maximum restoring force).
Key takeaways
  • Momentum and Impulse: using p = mv and impulse FΔt = Δp for impacts and safety design.
  • Momentum is conserved in every collision: Total momentum before an interaction equals total momentum after, provided no external impulse acts.
  • momentum: Mass × velocity (p = mv), a vector quantity measured in kg m/s.
  • Watch out for: treating momentum as a scalar
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